1. Field of the Invention
The invention relates to a method for controlling the diameter of a single crystal to a set point diameter during the pulling of the single crystal from a melt which is contained in a crucible.
2. Description of the Related Art
The CZ method is a method which is used on the industrial scale, in order for example to produce silicon single crystals which are processed further to form wafers. The wafers are needed as substrates for the production of electronic components. In order to produce a silicon single crystal by the CZ method, silicon is melted in a crucible, and a seed crystal is immersed in the melt and raised out from the melt. After the elimination of dislocations, the desired single crystal grows at the lower end of the seed crystal. The growth of the single crystal comprises a starting phase and an end phase, during which the diameter of the single crystal is increased and decreased, respectively. This is normally done by changing the lift rate with which the seed crystal is raised. During a phase between the starting phase and the end phase, efforts are made to keep the diameter of the single crystal as constant as possible, because only the section of the single crystal which is pulled during this phase is processed further to form wafers.
At the phase boundary on the edge of the single crystal, the melt forms a meniscus. The meniscus is a region in which the melt extends downward with a particular curvature from the phase boundary on the edge of the single crystal to the level of a surface of the melt outside the meniscus. The outer edge of the meniscus is the place where the meniscus reaches the level of the surface of the melt. The height of the meniscus is the vertical distance between the phase boundary and the level of the surface of the melt outside the meniscus. The phase boundary on the edge of the single crystal is the place where the growing single crystal, the melt and the surrounding atmosphere meet. A tangent to this phase boundary and to the meniscus makes an angle with the vertical, the value of which depends on the height of the meniscus.
Under ideal conditions, which represent cylindrical growth of the single crystal with a constant set point diameter of the single crystal, the single crystal grows with a growth rate which corresponds to the value of the lift rate, but is opposite to the direction of the lift rate. Under these conditions, the height of the meniscus corresponds to the height z0. The angle between the tangent to the meniscus and to the phase boundary and the vertical has the value β0 under these conditions.
If the height z of the meniscus or the meniscus angle β deviates from z0 or β0, respectively, the single crystal will grow inward or outward and the actual diameter Dcr of the single crystal will deviate from the set point diameter. With z>z0, or β<β0, the derivative of the diameter with respect to time will be dDcr/dt<0, or vice versa.
Various methods for controlling the diameter of a single crystal are known. For example, they may be distinguished by the variable manipulated for the control. In this context, control by means of the manipulated variable lift rate vp or the manipulated variable electrical power Lr of a heat source, which annularly encloses the single crystal, are to be highlighted. Both variants have the advantage that deviations of the diameter of the single crystal from the set point diameter can be reacted to with relatively fast response time. JP1096089 A2, WO 01/57294 A1 and US 2011/0126757 A1 contain examples of these methods.
US 2009/0064923 A1 describes a method in which the height of the meniscus is used in order to control the diameter, the height of the meniscus being derived by evaluating the brightness distribution in the course of the observation of a bright ring. The bright ring is a reflection on the meniscus, which is caused by neighboring components of the device for pulling the single crystal being reflected in the meniscus. Such components are in particular the crucible wall and the lower end of a heat shield, which usually encloses the single crystal, and, if present, a heat source which annularly encloses the single crystal. According to US 2009/0064923 A1, it is assumed that the position with the greatest brightness on the bright ring represents the location of the phase boundary on the edge of the single crystal, and the level of the surface of the melt outside the meniscus can be detected by means of the observed brightness distribution.
This assumption, however, is only an approximation of the physical situation. Furthermore, the fact that a short-term change in the height of the meniscus has no significant effect on the growth rate of the single crystal remains ignored. Accordingly, control of the diameter of the single crystal on the basis of the aforementioned method is inaccurate.